ED Experiments

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Transcript of ED Experiments

Page 1: ED Experiments

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Engineering dynamics

Submitted to: Madem Anam Anwar Submittedby:Muhammad umair 09-me-409

28/11/2010

786

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ENGINEERING DYNAMICS

EXPERIMENT 1Objective: To show that for a slider crank mechanism, the piston motion tends to perform SHM (Simple Harmonic Motion) with increasing value of connecting rod to crank ratio.

Apparatus:

Slider Crank Mechanism

Observations and Calculations

Connecting road=140mmCrank radius=55mmRatio= c.r / radius=2.54

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Application of crank cylinder mechanism:1:in reciprocating engines 2:in reciprocating compressors3:in scotch yoke4:in hand pump

Procedure: The experiment was completed in the following sequence:

1. The cylinder diameter was measured using the vernier calipers.

2. The inner diameter of the large and small ends of the conrod (Dlargeand Dsmall were measured using vernier calipers.

3. The crank was positioned such that the piston is at full elongiation,between the min and maximum strokes. Then the displacement of thepiston from the top of the cylinder was measured using vernier calipers.

4. The crank was rotated 10± anti-clockwise, and the new piston displacementwas measured using the vernier calipers and recorded in the logbook. Thisstep was repeated for 10± increments until one complete cycle (360± ofrotation) was completed.

5. Steps 3 and 4 were repeated twice and averages of these measurementswere calculated. The kinematic length of the crank, R, was then deter-mined from the average measurements

6. The crank was returned to the maximum position between Two stokes. The dial gauge was positioned over the inlet valve andthe reading on the dial gauge was recorded into the logbook.

7. The crank was turned 10± anti-clockwise and the the measurement on thedial gauge was recorded. (Note: It is necessary to correct the readingsfrom the dial gauge for the initial off set. This was done by subtractingthe reading on the dial when the shaft was fully closed from the otherreadings repeat tha experiment to eliminate errors

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Comments

1: The motion of the piston (for a constant crank angular velocity) is close to simple harmonic. This allows one to estimate the crank angle at which the maximum speed of the piston is obtained (for a constant crank angular veloc- ity). The maximum downward speed would occur at a crank angle of 90± andthe maximum upward speed would occur at a crank angle of 270±

2: it is used in oscilatinginng cylinder engine & crank sloted mechanism Due to its efficient transfer of power

3: it is also utilizes in withworth quick_return mechanism &rotary engines As it provide a best efficiency loop for it.

4: The kinematic motion of the slider in the slider-crank mechanism can be ex-pressed in terms of the lengths of the crank and the conrod, and the angulardisplacement of the crankshaft.

5: In vehicles The inlet valve was open during the intake stroke and the exhaust valve was open during the exhaust stroke. The opening range of both valves extended pastthe top-dead-centre postions for their respective strokes of the slider crank mechanism

6: The kinematic radius of the crank, R, is determined by halving the displacementof the piston from its maximum and minimum operating position.

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EXPERIMENT 2

Objective: To draw the work envelope of a 4-bar chain mechanism

Apparatus: 4bar chain mechanism

Theory: Kinematic pair A kinematic pair is the general name for two rigid bodies that can move with respect to each other via a mechanical constraint (joint) between the two bodies, with one or more degrees of freedom. In kinematics, one classifies the kinematic pairs in two groups:Lower pairs: the constraint is of the surface type. The following joint types exist: revolute joint ("pin", "hinge"), prismatic joint ("slider"), cylindrical joint, screw joint, planar joint, and ball joint or ball and socket joint.Higher pairs: the constraint is of the curve or point type. For example: cams or gears.Kinematic pairs are the building blocks of most kinematic chains and mechanical linkages, e.g., gimbals, robots, car suspensions.A kinematic pair must require these 2 conditions physical contact

Kinematic Pair Lower Pairs :Revolute joint · Prismatic joint · Cylindrical joint · Screw joint · Planar joint · Spherical joint

Higher Pairs :Cam · Gears4-bar chain mechanism : Plane linkg: (mechanical engineering) A plane linkage consisting of four links pinned tail to head in a closed loop with lower, or closed, joints.

A basic linkage mechanism used in machinery and mechanical equipment. The term has been applied to three types of linkages: plane, spherical, and skew.The plane four-bar linkage (Fig. 1) consists of four pin-connected links forming a closed loop, in which all pin axes are parallel. The spherical four-bar linkage consists of four pin-connected links forming a closed loop, in which all pin axes intersect at one point. The skew four-bar linkage (Fig. 2) consists of four jointed links forming a closed loop, in which crank 2 and link 4 are pin-connected to ground 1 and the axes of the pins are

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generally nonparallel and nonintersecting; coupler 3 is connected to crank 2 and link 4

by ball joints.

Plane four-bar linkage with joints at A, B, C, and D. φ, ψ, and μ are angles defining

orientations of joints.

perpendicular between axes of pin joints at A and D; φ, ψ, and ξ are angles defining orientations of joints.">Skew four-bar linkage with joints at A, B, C, and D. OA = f; ED = g; OE = common perpendicular between axes of pin joints at A and D; φ, ψ, and ξ are angles defining orientations of joints.Four-bar linkages are most frequently used to convert a uniform continuous rotation (the motion of crank 2) into a nonuniform rotation or oscillation (the motion of link 4). In instrument applications the primary function of the linkage is the conversion of motion, while in power applications both motion conversion and power transmission are fundamental.Each of the above linkages can be proportioned for three types of motion, or linkage types: crank-and-rocker, drag, and double-rocker.Crank-and-rocker linkages have a motion in which the crank (link 2) is capable of unlimited rotation, while the output link (link 4) oscillates or rocks through a fraction of one turn (usually less than 90°). This is the most common form of the plane and the skew four-bar linkage, and is used in machinery and appliances of all types.In drag linkages the motions of cranks 2 and 4 are both capable of unlimited rotations. The plane drag linkage has been used for quick-return motions. The most common drag linkage is the spherical drag linkage. One such linkage is the Hooke-type universal joint, or hooke joint. See also Universal joint.In double-rocker linkages, neither crank 2 nor 4 is capable of complete rotations. Such motions occur in hand tools and mechanical equipment in which only limited rotations are required. See also Linkage (mechanism); Straight-line mechanism. Kinematic InversionEvery mechanism has moving members which move relative to each other about the joints connecting them. These relative motions result in the trajectories of the points on

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members of the mechanism. In any mechanism one link or member is fixed and acts as the frame. The trajectories and motion characteristics of mechanism depend on the choice of the reference frame link.Inversions of a mechanism are the different configurations of the mechanism with change of the fixed reference link called frame. For different inversions of a mechanism although the motion characteristics are entirely different but the relative angular displacements of the members remain unchanged irrespective of the link chosen as frame.Determining the Inversions of a MechanismBefore going into details of obtaining inversions of a mechanism I would like to make it very clear that Inverse Kinematics is different from Kinematic Inversion. Read more about Inverse Kinematics.Every mechanism is formed of a kinematic chain. When one of the links in the kinematic chain is fixed it becomes a mechanism. To determine the inversions of a mechanism consider the kinematic chain forming the mechanism and obtain the desired inversions by fixing any one of the members as the frame link.Inversions of a Four-Bar MechanismA typical four bar mechanism, as the name denotes, is formed of a kinematic chain of four members connected by revolute joints. This mechanism can have four possible configurations with a different link fixed as frame each time.

Configuration 1Link 1 is taken as the base link or frame. In this configuration the shortest link is jointed to the base link and this joint can fully rotate and hence called as crank. The other link jointed to the base link oscillates and called as a rocker. This configuration of the four-bar kinematic chain is called as Crank-Rocker mechanism.

Configuration 2Link 2 is fixed as the base link. In this configuration shortest link is the base and both joints to the base can rotate completely. It is thus called as Double-Crank or a Drag-Link.

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Configuration 3Link 3 is fixed as the base link. It can be observed that this configuration is same as the Crank-Rocker mechanism.

Configuration 4Link 4 is fixed as the base link. In this configuration shortest link is the coupler and both the links connected to the base link cannot rotate fully, both oscillate. In this configuration the four-bar kinematic chain is called as Double-Rocker mechanism.

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Grashof's law is applied to pinned linkages and states; The sum of the shortest and longe t link of a planar four-bar linkage cannot be greater than the sum of remaining two links if there is to be continuous relative

Procedure Let , maximum distance b/w shaft and piston or circular dia=Frame=q=10cm, Driver/output=p=5cm, Coupler/connecting rod=L=7cm. Crank/input link =or dia of piston=s=3cm,

First, draw a straight line, 10 cm long (s).On one side of the line, draw a circle of radius=s, and divide it into 12 equal parts, and name them as 1, 2, 3….12.On the right edge of the line, draw a circle of radius=p.Open your compass to 7cm (l); keeping its needle on point 1, bisect it at the other circle (radius=p). Join this point of bisection to center of the circle of radius p. This is the coupler (l).Repeat the steps above for all points on the crank/input link circle.Draw three perpendicular lines of 1cm length, one on each of the topmost 3 paths of the coupler (l).Trace a line that touches the top of these three 1cm lines, starting at the input link circle and ending at output link circle Select the refrence straight line of 10 cm long (s).On the LHS of the line, draw a circle of radius=s, and divide it into 12 equal parts, naming the 12 edges as 1, 2, 3….12.On the right edge of the line, draw a circle of radius=p.Open your compass to 7cm (l); keeping its needle on point 1, bisect it at the other circle (radius=p). Join this point of bisection to center of the circle of radius p. This is the coupler (l).Repeat the steps above for all points on the crank/input link circle.Draw three perpendicular lines of 1cm length, one on each of the topmost 3 paths of the coupler (l).

. draw the line that meets the top of these three 1cm lines, starts from the input link circle and ending at output link circle

Comments:

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1: A 4- bar slider has six instantinous centers regardless of dimentionsor orientations of links

2: According to Grashof's law in the pined linkes the sum of the shortest and longest link of a planar four-bar linkage cannot be greater than the sum of remaining two links if there is to be continuous relative motion between the link

3:for afor bar with for pin joints four I’c are immediately inentified each four I’c is marked on circuleas a line drawn b/w two indices.these for I”c are actually not imaginary pin joints. In order to find other I’c we must apply Keniddy rule over and overe

EXPERIMENT 3

Objective: To investigate a 4-bar mechanism and to find the velocities of the follower/output link.

Apparatus: 4-bar mechanism

Theory:-Instantenous CenterThe instant centre of rotation, also called instantaneous centre, for a plane figure moving in a two dimensional plane is a point in its plane around which all other points on the figure, for one instant, are rotating. This point itself is the only point that is not moving at

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that instant. According to the Euler's rotation theorem any 3D rotation that has a fixed point also has a fixed axis. Therefore in 3D rotations it is more common to speak of the instant axis of rotation.

Extension of a rigid body: The extension of a rigid body refers to the operation of theoretically extending the body to fill all space. By this operation every point in space becomes a point of the body and as a result has a velocity associated with it. Since this is not an actual extension of the body, a theoretical extension does not influence how the actual body moves-it simply follows the motions of the actual body.Instantaneous Center of Velocity (ICV): Any point on a rigid body or on its extension that has zero velocity is called the Instantaneous Center of Velocity of the body. Assuming one knows the ICV of a body, one can calculate the velocity of any point A on the body using the equation v_A + W®/ icv +v icv and recognizing that be definition. This gibes

In 2-D motion, if is in the plane of motion and is perpendicular to this plane, then one can use the scalar relation Methods of finding the ICV:

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Given the velocity of point A on a rigid body and the angular velocity of the

rigid body one can use the above equation to find the distance between the point A and the ICV. One can then draw a line perpendicular to the velocity and passing through

A, and move along this line a distance to get to the ICV. The side on which the ICV is can be determined by the direction of the angular velocity. Given the velocity of points A and B on a rigid body one can find the ICV by

drawing a line perpendicular to and passing through A, and by drawing a line

perpendicular to and passing through B. One of the following three cases will result The lines intersect at one point: The point of intersection is the ICV. The angular velocity can be calculated once the ICV is determined using the velocity of either point and its corresponding distance from the ICV.

The lines are parallel (they intersect at infinity): The ICV is at infinity, and the angular velocity is zero since infinity times zero is the only way one can get velocities other than infinite. Therefore, the body is in pure translation and the velocity of the two points must be the same.

The two lines fall on top of each other: One can find the location of the ICV using the proportionality of velocity and distance from the ICV to create similar triangles. This follows from

Observations and calculations:

Length of crank=47.15

Frame member=150mm

Length of coupler=174mm

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Length of rocker=68.5

No of obs. Crank angle Θ Rocker angle Ø OAD1 0 68 162 20 75 233 40 83 364 60 92 425 80 102 466 100 115 507 120 127 478 140 140 43

Procedurefirst adjust tha apparatus on flate table and adjust the crank on any desired position andtake up the slack with the screws on the coupler but donot tighten.use a ruler to measure the length of tfhe crank,follower,rocker and frame members of the mechanism.Start with the crank at 0 degree and note the position of rocker.set the extra link with scale yo the same angle as the rocker.than read the distance Oad from the scale by noting where the the line in the centre of the follower crosses the scale.repeat the reading every 10 degree of the crank angle.

Graph

Comments

1: In biomechanical research the instant centre of rotation is observed for the functioning of the joints in the upper and lower extremities. For example in analysing the knee, ankle,[ or shoulder joints2: D uring experiment the readings should be clearly noted as shaft is slightly titled and it is difficult to take accurate readings3; The experimental apparatus should be well lubricated so that slider and shaft moves afficiently and without friction 4; Study of the joints of horses: "...velocity vectors determined from the instant centers of rotation indicated that the joint surfaces slide on each other."5; The braking characteristiscs of a car may be improved by varying the design of a brake pedal mechanism.6: it is used in Designing the suspension of a bicycle, or of a car.7; while drawing the graph we should locate point efficiently and accurately to getrealiable and accurate graph

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Experiment no 4

Objective: To draw displacement, velocity and acceleration graphs for slider crank mechanism.

Apparatus: Slider crank mechanism

Theory: θ=angular displacement of crankφ=angular displacement of connecting rodw=dθ/dt=angular velocity of crankNr=length of crankl=length of connecting rodΩ=angular velocity of crank.η=L/rangular analysis of slider crankx=OP-OP’ =(l+r)-(rcos θ+lcos φ)

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= -l(1-cos φ)+(r(1-cos θ) =r(1-cos θ)+l(1-cos φ) =r+l-r cos θ -l cos φIn both triangles components are equalrsin θ=lsinφr/l sinθ=sinφ L/r=n1/n sinθ=sinφCosφ=√(1 – sin2φ)Cosφ = √(1 – (sin2 θ)/n2)

Cosφ = √(1 – (sin2 θ)/2n2)X = r(1-cosθ) + L(1-1+ sin2 θ)/2n2) = r(1-cosθ) + L( sin2 θ)/2n2) = r(1-cosθ) - r( sin2 θ)/2n) = r(1-cosθ) - r( 1 – cos2θ)/4n) = r [ 1 – cosθ – (1- cosθ)/4n] dx/dt = r(sinθ + (sin2θ)/2n) dθ/dt = wr(sinθ + sin2θ) = w2r (cosθ + (cos2θ)/n) .

Observations and CalculationsConnecting road=140mmCrank radius=55mmRatio= c.r / radius=2.54

Procedure: The experiment was completed in the following sequence:

The cylinder diameter was measured using the vernier calipers. The inner diameter of the large and small ends of the conrod (Dlargeand Dsmall were measured using vernier calipers.

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.The crank was positioned such that the piston is at top full elongiation,between the min and maximum strokes. Then the displacement of thepiston from the top of the cylinder was measured using vernier calipers. The crank was rotated 10 degree anti-clockwise, and the new piston displacementwas measured using the vernier calipers and recorded in the logbook. Thisstep was repeated for 10 degree increments until one complete cycle (360± of

rotation) was completed. Steps 3 and 4 were repeated twice and averages of these measurementswere calculated. The kinematic length of the crank, R, was then deter-mined from the average measurements The crank was returned to the maximum position between Two stokes. The dial gauge was positioned over the inlet valve andthe reading on the dial gauge was recorded into the logbook. The crank was turned 10± anti-clockwise and the the measurement on thedial gauge was recorded. (Note: It is necessary to correct the readingsfrom the dial gauge for the initial off set. This was done by subtractingthe reading on the dial when the shaft was fully closed from the otherreadings repeat tha experiment to eliminate errors

Comments:

1:It is obvious from graph that at initial point the displacement of crank is max an it reduce with the increasing angle upto 180 and reaches the main value and after that displacement increases upti360 degree2: The kinematic radius of the crank, R, is determined by halving the displacementof the piston from its maximum and minimum operating position.3: The kinematic motion of the slider in the slider-crank mechanism can be ex-pressed in terms of the lengths of the crank and the conrod, and the angulardisplacement of the crankshaft.4:The value of displacement is inaccurate if not read properly just in top front of scale and desired results are not found 5:The velocity is determine from displacement and Ǿ graph by sketchinh right velocity vector to every instantaneous displacement